3 - Open and closed sets

[@Ibrahmoment]

THE best video on open sets and closed sets. Very informative and concise. I really wish you'd have also introduced "boundary" of a set, especially since it slightly aids in developing intuition for open and closed sets. With that, the video would have been truly complete.

[@frankswenton3177]

Thanks! Boundary would have been good to include, but the content we were covering for the Real Analysis class didn't really need it, so I left it out to help keep the length down. If this were for a Topology class proper, that definitely would have made it in---along with the bits about decomposing a space into the interior of a set, the boundary of the set, and the interior of its complement, the closures of each side being the disjoint unions of the interiors and the boundaries etc. I might add to this video sequence eventually (I ran out of time to make what would have been the next videos on compactness, connectedness, metric completeness, etc. that semester)!

[@NewDeal1917]

This has to be the best video on KZbin devoted to the subject. Let me elaborate: 1) Production quality is great. Clear audio, distinct voice, no annoying accent or background noise. Animations and illustrations seem right at their place, which is often not the case with other slide based presentations. 2) Great insights and intuition. Instead of unleashing a somewhat usual formalized hellfire, you manage to convey the core motivation behind every idea. Most of the time after having a lecture I feel the need to clarify some concepts going to Stackexchange or Mathoverflow, yet with your videos I don't feel the need. 3) Unlike some popular mathbloggers you don't stop at bare intuition, but go all the way, providing all the formal statements and derivations in a way that enhances understanding, not drowning it in symbolic nightmare. That's how true education (and not just science realted entertainment) should be done. Do you have any plans for further videos? Perhaps some measure theory, global topology, even integration theory or differential equations? I admire you talent and approach. Well, I'd gladly pay for such content, hope you have Patreon or something? Thanks again, that's exceptional!